Pulse shaping and ultrashort laser pulse filamentation for applications in extreme nonlinear optics.

This thesis deals with numerical studies of the properties and applications of spatio-temporally coupled pulses, conical wavepackets and laser filaments, in strongly nonlinear processes, such as harmonic generation and pulse reshaping. We study the energy redistribution inside these wavepackets propagating in gases and condensed media, in the linear and nonlinear regime. The energy flux constitutes a diagnostic for space-time couplings that we applied to actual experimental results. We analyze the spectral evolution of filaments in gases and derive the conditions for the generation of ultrashort pulses in the UV range. We study high harmonic generation in a gas from ultrashort conical wavepackets. In particular, we show how their propagation properties influence the harmonic output. We also study the interference of different electron trajectories. Finally, we derive the shape of stationary Airy beams in the nonlinear regime. For each topic, we present experimental results that motivated our works or were motivated by our simulations.